Imaging systems and methods for recovering object visibility

ABSTRACT

A system and method are provided for imaging in scattering media such as fog, water and biological tissues. Normally, such images suffer from poor visibility due to backscattering and signal attenuation. At least two images are taken of the scene using active widefield polarized illumination, with different states of a camera-mounted polarizer. The degree of polarization of backscatter is estimated in every point of the scene, leading to an estimation of the backscatter in every point of the scene. A portion or all of the value of backscatter can be deducted in each point of the scene resulting in an enhanced image with improved contrast and brightness range across the field of view.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a national stage of international applicationPCT/IL2007/000560, filed 9 May 2007. Additionally, this applicationclaims the benefit of U.S. Provisional Application No. 60/798,737, filed9 May 2006.

FIELD OF THE INVENTION

The present invention relates to systems and methods for photographingan object and in particular for photographing an object immersed in ascattering medium such as water, fog or biological tissues.

BACKGROUND OF THE INVENTION

1. Scattering Media

A wide range of imaging domains exists in scattering media. Severalstudies [P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D.L. Jordan, and J. G. Walker. Improving visibility depth in passiveunderwater imaging by use of polarization. App. Opt., 42:2794-2803,2003.; E. Namer and Y. Y. Schechner. Advanced visibility improvementbased on polarization filtered images. In Proc. SPIE 5888: PolarizationScience and Remote Sensing II, pages 36-45, 2005.; Y. Y. Schechner andN. Karpel. Clear underwater vision. In Proc. IEEE CVPR, volume 1, pages536-543, 2004.; Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar.Polarization-based vision through haze. App. Opt., 42:511-525, 2003.; S.Shwartz, E. Namer, and Y. Y. Schechner. Blind haze separation. In Proc.IEEE CVPR, 2006] improved visibility in such media under naturalillumination. However, natural light is in general unavailable inrelevant scenarios, as in deep water, pipelines, night and biologicaltissues. Moreover, natural illumination may change in time unpredictably[Y. Y. Schechner and N. Karpel. Attenuating natural flicker patterns. InProc. MTS/IEEE OCEANS, pages 1262-1268, 2004]. The need to useartificial illumination is therefore obvious. This involves a practicaldifficulty: the illumination is strongly scattered back towards thecamera from particles along the line of sight (LOS), creatingbackscatter, as shown in FIG. 1. The backscatter overwhelms the signal,causing severe loss of visibility. This problem can be alleviated byincreasing the baseline between the light source and the camera [J. S.Jaffe. Computer modelling and the design of optimal underwater imagingsystems. IEEE J. Oceanic Eng., 15:101-111, 1990.; B. Skerry and H. Hall.Successful Underwater Photography. New York: Amphoto books, 2002].However, this is impossible to do in tight environments such asshipwrecks or pipelines. Moreover, a construction using long strobe armsis cumbersome and less hydrodynamic. In any case, backscatter ultimatelyovercomes the attenuated signal for far enough objects, no matter howfar the light source is placed. Backscatter can be modulated and thencompensated for in image post-processing. Such current methods requireacquisition of long image sequences by structured light [D. M. Kocak andF. M. Caimi. The current art of underwater imaging with a glimpse of thepast. MTS Journal, 39:5-26, 2005; M. Levoy, B. Chen, V. Vaish, M.Horowitz, I. McDowall, and M. Bolas. Synthetic aperture confocalimaging. ACM TOG, 23:825-834, 2004; S. G. Narasimhan, S. K. Nayar, B.Sun, and S. J. Koppal. Structured light in scattering media. In Proc.IEEE ICCV, volume 1, pages 420-427, 2005] or time-gating [S. G. Demosand R. R. Alfano. Temporal gating in highly scattering media by thedegree of optical polarization. Opt. Letters, 21:161-163, 1996; G. R.Fournier, D. Bonnier, L. J. Forand, and P. W. Pace. Range-gatedunderwater laser imaging system. Opt. Eng, 32:2185-2190, 1993; Harsdorf,R. Reuter, and S. Tonebon. Contrast-enhanced optical imaging ofsubmersible targets. In Proc. SPIE, volume 3821, pages 378-383, 1999; M.P. Strand. Imaging model for underwater range-gated imaging systems. InProc. SPIE, volume 1537, pages 151-160, 1991; B. A. Swartz and J. D.Cummings. Laser range-gated underwater imaging including polarizationdiscrimination. In Proc. SPIE., volume 1537, pages 42-56, 1991]. Suchsequences may lengthen the overall acquisition time. Moreover, suchsystems have the drawback of being very complex and expensive.

SUMMARY OF THE INVENTION

To counter the problems, the present invention looks at widefield (notscanning) illumination with a small (or no) baseline, where thebackscatter is modulated by polarization. Preliminary studies by others[G. C. Giakos. Active backscattered optical polarimetric imaging ofscattered targets. In IEEE Instr. & Measurement Tech. Conf, volume 1,pages 430-432, 2004; G. D. Gilbert and J. C. Pernicka. Improvement ofunderwater visibility by reduction of backscatter with a circularpolarization technique. App. Opt., 6:741-746, 1967; G. D. Lewis, D. L.Jordan, and P. J. Roberts. Backscattering target detection in a turbidmedium by polarization discrimination. App. Opt., 38:3937-3944, 1999]indicated that backscatter can be reduced by polarization. However, thepresent invention goes further. Using post-processing means, it ispossible to remove residual backscatter that is not blocked by opticalmeans. Moreover, a rough estimate of the 3D scene structure may beobtained from the acquired frames. The acquisition setup is a simplemodification of instruments used routinely in such media: simplymounting two polarizers, one on the light source and another on thecamera. The acquisition process is instantaneous, i.e., requiring onlytwo frames, rather than scanning.

The approach is based on several insights into the image formationprocess. The invention shows that backscatter and attenuation ofartificial illumination can be well approximated by simple closed-formparametric expressions. To incorporate polarization, we have performedempirical polarization measurements in real underwater scenes: in atemperate latitude sea (Mediterranean Sea), a tropical sea (the RedSea), in a murky lake (Sea of Galilee) and a swimming pool.

The present invention thus relates to an imaging method and system forrecovering object visibility in a scene containing a scattering medium.The method comprises the following steps:

-   -   (i) illuminating the scene with an active illumination system on        which a polarizer is mounted;    -   (ii) mounting a polarization analyzer on an image acquisition        equipment;    -   (iii) acquiring a first frame of the scene;    -   (iv) changing the polarization state of the polarizer or of the        polarization analyzer or of both;    -   (v) acquiring one or more additional frames of the scene;    -   (vi) estimating the degree of polarization of backscatter in        every point of the scene;    -   (vii) estimating the backscatter in every point of the scene        based on the analysis performed in (vi); and    -   (viii) deducting a portion or all of the value of the        backscatter in each point of the scene to receive one or more        enhanced images with improved contrast and brightness range        across the field of view.

The illumination system can include one or more light sources. The lightsources use an active, widefield illumination as opposed toscanning-methods lighting.

In one embodiment of the present invention, the first frame of the sceneis acquired with the polarizer or the polarization analyzer in apolarization state with an approximate minimum or low visiblebackscatter. In another embodiment of the present invention, the one ormore additional frames of the scene are acquired with the polarizer orthe polarization analyzer in a polarization state with approximatelymaximum or high visible backscatter. It is not necessary to use theabsolute minimum or maximum backscatter value, but using a relativelylow amount and a relatively high amount of backscatter can produce goodresults.

The present invention also compensates for signal attenuation.

In a further embodiment of the present invention, the enhanced image isfurther combined with one or more images obtained by any method adaptedfor enhancing images of polarizing objects. Estimating the object'spolarization usually assumes that the object returns a fixedpolarization value.

The present invention's active illumination system can include at leastone of the following for better performance:

-   -   (i) a multi-polarized light source composed of a polarized array        of light sources so that at least one portion of the light        sources are polarized in a different polarization state compared        to the polarization state of the remaining light sources, and        each frame is acquired using different polarization of the        illumination;    -   (ii) one or more optical filters are attached to a light source        with a gap between the light source and the polarizer and        analyzer so that the surrounding medium can fill in the gaps,        providing natural cooling to the system; and    -   (iii) devices that convert more than half the energy into        polarized light.

Light Emitting Diodes (LED's) are a good example of an available lightsource, though other lighting means can also be used by the invention.

Examples of optical filters include but are not limited to polarizers,diffusers and the like.

In one embodiment of the present invention, the polarization analyzer ismounted on an imaging sensor comprised of a plurality of pixels, so thatthe polarization analyzer mounted on one portion of the pixels is in onepolarization state. The remaining pixels may have a polarizationanalyzer mounted, or may be without a polarization analyzer. Thepolarization analyzer mounted on the remaining pixels of the imagingsensor is in one or more different polarization states. The polarizationanalyzer is mounted on a plurality of pixels, but not necessarily on allof the pixels. One portion of the pixels, for example, half the pixels,can have the polarization analyzer in one polarization state while theother pixels have a polarization analyzer mounted with a differentpolarization state.

The active illumination system of the invention can be calibrated formedium and light properties by acquiring one or more calibration framesof the scene wherein at least one calibration frame contains a knownobject. The known object can be black or a non-black object can also beused.

For example, medium and light properties can be calibrated using thefollowing steps:

-   -   (i) acquiring a first calibrating frame of a black object        situated in a first distance from an image acquisition        equipment;    -   (ii) acquiring a second calibrating frame of the black object        situated in a second distance from the image acquisition        equipment;    -   (iii) acquiring a third calibration frame of an illuminated void        region in the scene, with no objects in sight; and    -   (iv) deriving calibration parameters based on the first, second        and third calibration frames.

The derived calibration parameters are useful for estimating thedistances between objects in the scene. 3D reconstruction of the sceneis most effective in short ranges when light still exists in sufficientintensity and the backscatter has not saturated and still variesrapidly.

In a further embodiment of the present invention, the method estimatesand compensates for falloff. Backscatter is related to an object'sdistance from the camera.

In another aspect of the present invention, an imaging method isprovided for calibration of light properties by acquiring one or morecalibration frames of a scene wherein at least one calibration framecontains a known object.

In one embodiment of the present invention, an imaging method isprovided for calibration of light properties by:

-   -   (i) acquiring a first calibrating frame of a known object        situated in a first distance from an image acquisition        equipment;    -   (ii) acquiring a second calibrating frame of the known object        situated in a second distance from the image acquisition        equipment;    -   (iii) acquiring a third calibration frame of an illuminated void        region in the scene, with no objects in sight; and    -   (iv) deriving calibration parameters based on the first, second        and third calibration frames.

Calibration can also be achieved by imaging two different boards in twodistinct distances; and deriving calibration parameters based ona-priori known ratio between the albedos of the two different boards.

A third calibration system can be achieved using the polarizationtechnique. Thus in another embodiment of the present invention, animaging system is proposed, comprising:

-   -   (i) means for illuminating the scene with an active illumination        system on which a polarizer is mounted;    -   (ii) means for mounting a polarization analyzer on an image        acquisition equipment;    -   (iii) means for acquiring a first frame of the scene;    -   (iv) means for changing the polarization state of the polarizer        or of the polarization analyzer or of both;    -   (v) means for acquiring one or more additional frames of the        scene;    -   (vi) means for estimating the degree of polarization of        backscatter in every point of the scene; and    -   (vii) means for estimating the backscatter in every point of the        scene based on the analysis performed in (vi).

Preferably, images taken are of a board having all its pixels in thesame distance from the image acquisition equipment

In another aspect, the invention relates to fusion techniques in orderto recover object visibility in a scene containing a scattering medium.In one embodiment, a fusion imaging method is proposed for enhancingobject visibility in a scene containing a scattering medium, the methodcomprising the steps of:

-   -   (i) illuminating the scene with an active illumination system        and acquiring a first image of the scene;    -   (ii) acquiring one or more additional images of the scene such        that each image is taken with a different illumination of the        scene; and    -   (iii) applying a fusion technique using each image components to        obtain an image with enhanced contrast, color and/or visibility.

The present invention can use any fusion technique of the art in orderto obtain an enhanced image. For example, one fusion technique comprisesthe following steps:

-   -   (i) decomposing each image into a Gaussian and a Laplacian        pyramid;    -   (ii) creating a new Laplacian pyramid, in which each level is        composed of values from the corresponding level in the Laplacian        pyramids of all the images; and    -   (iii) decoding the final image using the new pyramid.

The different illumination of the scene refers to changes in the spatialand/or directional distribution of the illumination of the scene as canbe obtained, for example, by changing the position and/or angle ofeither or both of the illumination system (i.e. flash light) or imageacquisition equipment (i.e. camera).

Optionally, the method can also comprise the step of assigning the baselevel of the Laplacian pyramid a constant value which is the average ofall pixel values of all base levels before step (v). Alternatively,other methods can be used for assigning a value to the base level of theLaplacian pyramid such as the by-pixel average of the base levels of theimages.

Preferably, the maximum level N is a parameter such that the base levelof the Laplacian pyramid is approximately 4 pixels by 4.

In yet another aspect of the present invention, an imaging method isprovided for recovering object visibility in a scene of a scatteringmedium, the method comprising the steps of:

-   -   (i) illuminating a scene in a scattering medium using an        illumination system;    -   (ii) acquiring a first frame of the scene with an image        acquisition equipment;    -   (iii) acquiring a second frame of either:        -   an illuminated void region in the scene, with no objects in            sight;        -   a black object in the scene; or        -   a computer simulation of the backscatter value at each pixel            based on knowledge of the scene structure or an equivalent            analytical calculation; and    -   (iv) subtracting a portion or all of the second frame from the        first frame to receive an enhanced image with improved contrast        and brightness range across the field of view.

Since the second frame contains no object, it shows the full backscatterof the scene. The second frame can thus be subtracted from any image ofan object taken from the scene, in order to receive a clearer image.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1 shows an underwater image taken in the Mediterranean Sea with twoartificial light sources according to prior art techniques.

FIG. 2 shows a basic camera and illumination setup according to theinvention.

FIG. 3 shows an actively illuminated scene depicting three pictures: aclear image (top), a signal derived from the object in the picture(left), and the complete scene with backscatter (right).

FIG. 4 is a graph showing the backscatter given by Eq. (10) asapproximated by Eq. (12), with c=0:1 m⁻¹.

FIG. 5 is a picture showing scuba diving with a lift bag towards nightexperiments in the Red Sea.

FIG. 6 is a single-lamphead version of the system of the invention.

FIG. 7A shows a scene corresponding to FIG. 1 after applying thebackscatter removal method of the invention. FIG. 7B shows the estimatedbackscatter of the same scene.

FIGS. 8A-B show images taken in the Sea of Galilee with the system ofthe invention using one light source at the top. FIGS. 8C-D show theresults of applying the method of the invention to the images taken.

FIG. 9 is a graph showing normalized falloff as a typical function ofthe backscatter in an arbitrary pixel.

FIGS. 10A-D show simulated backscatter removal, 3D recovery and falloffcompensation of a noisy object.

FIG. 11 is a polarized array of LEDs, where half of the LEDs arepolarized perpendicular to the other LEDs.

FIG. 12 shows a natural water cooling mechanism of the light source.

FIGS. 13A-B are an image of {circumflex over (B)}/B_(∞) for anunderwater scene. FIG. 13A: assuming p_(obj)=0. FIG. 13B: Using anestimated p_(obj).

FIG. 14A is a scene with a polarized reflection from an object. FIG. 14Bis an image wherein the value of {circumflex over (B)} is extractedassuming p_(obj)=0. FIG. 14C shows B_(∞), wherein MI is calculatedbetween {circumflex over (B)} and Ŝ using different values of p_(obj)=0.FIG. 14D is an image with correct value of {circumflex over (B)}. FIG.14E is a graph of MI between {circumflex over (B)} and Ŝ in each channel(R, G, B).

FIG. 15 is an estimation of a distance map in different elevations.

FIG. 16 shows an image of a scene taken with an upper light source.

FIG. 17 shows an image of the scene of FIG. 16 taken with a lower lightsource.

FIG. 18 shows an improved image wherein FIGS. 16 and 17 are addedtogether.

FIG. 19 shows an improved image wherein FIGS. 16 and 17 are fusedtogether according to the invention.

FIG. 20 shows an image of a scene taken with an upper light source.

FIG. 21 shows an image of the scene of FIG. 20 taken with a lower lightsource.

FIG. 22 shows an improved image wherein FIGS. 20 and 21 are addedtogether.

FIG. 23 shows an improved image wherein FIGS. 20 and 21 are fusedtogether according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

In the following detailed description of various embodiments, referenceis made to the accompanying drawings that form a part thereof, and inwhich are shown by way of illustration specific embodiments in which theinvention may be practiced. It is understood that other embodiments maybe utilized and structural changes may be made without departing fromthe scope of the present invention.

2. Theoretical Background

2.1 Artificial Illumination

Consider a camera in a scattering medium. At pixel (x; y), the measuredimage I(x; y) is the sum of the object signal S(x; y) and a backscattercomponent B(x; y),I(x,y)=S(x,y)+B(x,y).  (1)We now detail these components. Let z be the axial distance from thecamera of a point in the volume. This scene point is at a distanceR_(source) (x, y, z) from a light source which resides by the camera.The source radiance is L^(source). The irradiance of the scene point [J.S. Jaffe. Computer modeling and the design of optimal underwater imagingsystems. IEEE J. Oceanic Eng., 15:101-111, 1990] due to this source is

$\begin{matrix}{{I^{source}\left( {x,y,z} \right)} = {L^{source}{\frac{\exp\left\lbrack {- {{cR}_{source}\left( {x,y,z} \right)}} \right\rbrack}{R_{source}^{2}\left( {x,y,z} \right)}.}}} & (2)\end{matrix}$Eq. (2) is affected by the medium, which is characterized by anattenuation coefficient c and by the 1/R² _(source) falloff caused byfree space propagation.Here c=a+b, where a is the absorption coefficient of the medium and b isits total scattering coefficient. The latter expresses the ability of aninfinitesimal medium volume to scatter flux in all directions.Integrating over all solid angles Θ,

$\begin{matrix}{{b = {{\int_{\Theta}^{\;}{{b(\Theta)}\ {\mathbb{d}\Omega}}} = {2\;\pi}}}{{\int_{0}^{\pi}{{b(\theta)}{\sin(\theta)}\ {\mathbb{d}\theta}}};}} & (3)\end{matrix}$where θε[0,π] is the scattering angle relative to the propagationdirection [C. D. Mobley. Light and Water: Radiative Transfer in NaturalWaters, chapter 3,5. San-Diego: Academic Press, 1994]. Note that thevariables a; b(θ) and c are all functions of the wavelength. The rangeθε[0,π/2) corresponds to forward scattering, while θε[π/2,π] correspondsto backscattering.

Since the camera is beside the artificial illumination source, it isbackscatter that affects the sensed image most. It is a result ofaccumulation [J. S. Jaffe. Computer modeling and the design of optimalunderwater imaging systems. IEEE J. Oceanic Eng., 15:101-111, 1990; B.L. McGlamery. A computer model for underwater camera system. In Proc.SPIE, volume 208, pages 221-231, 1979] of all backscattered light alongthe line of sight (LOS). Any backscattering from a particle in themedium undergoes attenuation in the distance. FIG. 2 shows a basiccamera 10 and illumination setup according to the invention. The camera10 comprises an analyzer 20 and the illumination system comprises alamphead 30 and a polarizer 40. R_(cam)—distance of a point from thecamera 10; R_(source)—distance of a point from a light source;R_(sc)—baseline; θ—scattering angle; γ—angle between baseline and LOS;x, y—image coordinates; z—axial coordinate; Z₀—axial distance to firstintersection of light with the LOS.R _(cam)=√{square root over ((αx)²+(αy)² +z ²)}{square root over((αx)²+(αy)² +z ²)}  (4)between that particle and the camera 10, where α(z) is the camera 10magnification. Integrating all these scattering incidences,

$\begin{matrix}{{B\left( {x,y} \right)} = {\int_{0}^{Z_{obj}{({x,y})}}{{b\left\lbrack {\theta(z)} \right\rbrack}{I^{source}(z)}{\exp\left\lbrack {- {{cR}_{cam}(z)}} \right\rbrack}\ {{\mathbb{d}z}.}}}} & (5)\end{matrix}$The integration stops where an object is encountered in a distanceZ_(obj). Note that θ, I^(source) and R_(cam) all change with z.Moreover, they all depend on (x, y).2.2 Object Signal

Define L_(object)(x, y) as the object radiance we would have sensed hadno falloff occurred (as if scene irradiance is done by a distant source,with no attenuating media). The object irradiance suffers [J. S. Jaffe.Computer modelling and the design of optimal underwater imaging systems.IEEE J. Oceanic Eng., 15:101-111, 1990; B. L. McGlamery. A computermodel for underwater camera system. In Proc. SPIE, volume 208, pages221-231, 1979] from falloff as described in Eq. (2). Blur due to forwardscattering affects image quality less than the other effects [Y. Y.Schechner and N. Karpel. Clear underwater vision. In Proc. IEEE CVPR,volume 1, pages 536-543, 2004]. Light reflected from the object thenundergoes attenuation along the LOS. We define a falloff function

$\begin{matrix}{{F\left( {x,y} \right)} = {\frac{{\mathbb{e}}^{- {c{\lbrack{{R_{source}({x,y,Z_{obj}})} + {R_{cam}({x,y,Z_{obj}})}}\rbrack}}}}{R_{source}^{2}\left( {x,y,Z_{obj}} \right)}.}} & (6)\end{matrix}$Hence, the signal originating from the object isS(x,y)=L ^(object)(x,y)F(x,y).  (7)2.3 Active Polarization Imaging

By mounting a polarizer 40 on the light source, we polarize theillumination (see [E. Hecht. Optics, chapter 8,13. Addison Wesley, 4thedition, 2002] for polarization definitions). This light is thenbackscattered by particles in the medium. Had the backscattered lightbeen completely polarized, it could have been optically eliminated by acamera 10 mounted polarizer 40 (an analyzer 20). However, backscatteringinvolves some depolarization, i.e., some energy of the light becomesunpolarized, hence cannot be blocked by an analyzer 20. Nevertheless, asubstantial degree of polarization (DOP) is maintained uponbackscattering. The invention exploits this phenomenon. Once light isbackscattered, it propagates through the scattering medium towards thecamera 10. During this propagation, it further depolarizes [N. Shashar,S. Sabbah, and T. W. Cronin. Transmission of linearly polarized light inseawater: implications for polarization signaling. J. Exper. Biology,207:3619-3628, 2004]. This process is complex and depends on thedistribution of particle types and sizes and polarization type [. Jarry,E. Steimer, V. Damaschini, M. Epifanie, M. Ju-rczak, and R. Kaiser.Coherence and polarization of light propagating through scattering mediaand biological tissues. App. Opt., 37:7357-7367, 1998; G. W. Kattawarand M. J. Rakovic. Virtues of Mueller Matrix Imaging for UnderwaterTarget Detection. App. Opt., 38:64316438, 1999; F. C. MacKintosh, J. X.Zhu, D. J. Pine, and D. A. Weitz. Polarization memory of multiplyscattered light. Phys. Rev. B 40, 13:9342-9345, 1989; V. Sankaran, J. T.Walsh, and D. J. Maitland. Comparative study of polarized lightpropagation in biologic tissues. J. Biomed. Opt., 7:300-306, 2002]. Apreliminary empirical study [. D. Gilbert and J. C. Pernicka.Improvement of underwater visibility by reduction of backscatter with acircular polarization technique. App. Opt., 6:741-746, 1967] showed thatif the illumination is circularly polarized, then a significantimprovement of contrast can be achieved optically in water. The bottomline, however, is that this phenomenon is not well modeled yet for mostreal world media.

3 Scene Rendering

To make scene reconstruction tractable, we sought approximations. Weobtained this by rendering underwater scenes based on the models of Sec.2. This enabled us to gauge the importance of various effects and setupparameters, such as camera 10 illuminator baseline, scene range, mediumcoefficients, illumination spectrum and angular non-uniformity of thelight source.

For experimentation purposes, rendering relied on the properties of aNikon D100, a 20 mm lens and the spectrum of a 100 W Quartz TungstenHalogen bulb [Newport. Oriel Light Resources, 2004. p. I-28]. Forexample, the simulated source in FIG. 3 is placed 14 cm to theupper-right of the camera 10 lens, with its axis parallel to the camera10 axis. The angular spread and non-uniformity of the source are similarto those of the one we used in experiments. The rest of the parameterswere variable. The scene was assigned a distance map, e.g., varyinglinearly with y in the range 0.5-4.5 m.

FIG. 3 shows a clear image L^(object). Here we used oceanic watercharacteristics (absorption and scattering specifications) as in [C. D.Mobley. Light and Water: Radiative Transfer in Natural Waters, chapter3,5. San-Diego: Academic Press, 1994]. A signal derived from this objectis shown as well, next to the corresponding image I. It is clear thatbackscatter overwhelms the farther regions of the object. Moreover,these rendered images illustrate the non-uniformity of the backscatterand scene illumination caused by the falloff.

4 Assumptions and Approximations

For efficient rendering as well as reconstruction, it is beneficial tomake some assumptions and approximations.

-   -   Depolarization—As a default, we assume that depolarization due        to propagation is not significant, since effective propagation        distances are rather short in widefield artificial illumination        [B. Skerry and H. Hall. Successful Underwater Photography. New        York: Amphoto books, 2002], due to the falloff function (Eq. 6).    -   The object's signal. The method works best when S is unpolarized        as explained in [Y. Y. Schechner and N. Karpel. Recovery of        underwater visibility and structure by polarization analysis.        IEEE J. Oceanic Eng., 30:570-587, 2005].    -   Uniform backscatter coefficient—In the following, we mainly        refer to oceanic water. In this environment, according to [A. A.        Kokhanovsky. Light Scattering Media Optics, page 200. Springer,        3rd edition, 2004], the function b(θ) is insensitive to θ at        backscatter angles (θ≧π/2). Hence, we denote its typical value        as {tilde over (b)}. This simplifies the backscatter        integrations.    -   A closed form parametric expression for the backscatter        integral—Before we justify this in general, let us first        consider a special case in which the camera 10 illuminator        baseline is very small, relative to the object distance. In this        case,        R _(source)(x,y)≈R _(cam)(x,y).  (8)        Hence,

$\begin{matrix}{{{F_{approx}\left( {x,y,z} \right)} = \frac{\exp\left\lbrack {{- 2}\;{{cR}_{cam}\left( {x,y,z} \right)}} \right\rbrack}{R_{cam}^{2}\left( {x,y,z} \right)}},{and}} & (9) \\{{B\left( {x,y} \right)} \approx {\overset{\sim}{b}L^{source}{\int_{Z_{0}{({x,y})}}^{Z{({x,y})}}{{F_{approx}\left( {x,y,z} \right)}\ {{\mathbb{d}z}.}}}}} & (10)\end{matrix}$Note that the integration does not start at z=0. The reason is thatlight from the source does not illuminate the space interfacing with thecamera 10 lens. Rather, there is a minimum distance Z₀, at which lightrays from the illumination source intersect the LOS. If the light coneemitted by the illuminator was sharp, then Z₀ could have beengeometrically calculated. The range z<Z₀ is effectively dark, andtherefore does not contribute to the backscatter. Note that Z₀ is afunction of the pixel coordinate (x, y).

An analytic solution to the integral in Eq. (10) is given as the series

$\begin{matrix}{\frac{B}{\overset{\sim}{b}L^{source}} \approx {\left\lbrack {{- \frac{{\mathbb{e}}^{{- 2}\;{cz}}}{z}} - {2\; c\;\ln\; z} - {2\; c{\sum\limits_{n = 1}^{\infty}\frac{\left( {{- 2}\;{cz}} \right)^{n}}{n \cdot {n!}}}}} \right\rbrack_{z = Z_{0}}^{z = Z}.}} & (11)\end{matrix}$

Now, consider a special case where Z(x, y)=∞, i.e., effectively there isno object in front of the camera 10 at (x, y). Denote the backscattervalue there as B_(∞) (x, y).

We found in extensive numerical simulations, that Eq. (11) can be wellapproximated asB≈B _(∞){1−exp[−k(Z−Z ₀)]}  (12)where k is a parameter that depends only on c and {tilde over (b)} for agiven Z₀. An example is shown in FIG. 4, for a particular setup. Eq.(12) is simple. It has three parameters: an offset Z₀; a slope near Z₀,which is dictated by k, and a saturation value B_(∞). We use thisapproximation in our subsequent derivations.

In general, the setup is more complicated: a light source is not coaxialwith the camera 10, it is very non-uniform and there are severalsources, generally. Hence we simulated the backscatter resulting fromsuch systems being in the medium. Even then, we discovered throughsimulations that the numerical integration of backscatter still followsthe approximated model expressed in Eq. (12). The only difference isthat the parameters Z₀, k and B_(∞) vary with (x, y). To conclude, weuse Eq. (12) for backscatter caused by a general active illuminationsystem in the medium. To work with the model, however, its parametersneed to be determined per pixel. Next, we describe how they can becalibrated in-situ.

Note that [B. Sun, R. Ramamoorthi, S. Narasimhan, and S. Nayar. Apractical analytic single scattering model for real time rendering. ACMTOG, 24:1040-1049, 2005] simplified the integral in Eq. (5) to a closedform containing values obtained from a pre-calculated lookup table. Thisexpression is less useful when aiming to invert the process and is verysensitive to noise in the measurements.

Model Calibration

Suppose we have an uncalibrated active illumination system in a mediumhaving unknown characteristics. How can we determine the parameters Z₀,k and B_(∞) for each pixel (x, y)? Note that B_(∞) (x, y) can be easilyobtained: rigidly shift the camera 10/illuminator system, to take aphotograph of a void region in the medium (where no object is in sight).The acquired image is simply B_(∞) (x, y).

We are left with two unknowns per pixel, Z₀ (x, y) and k(x, y). Thesecan be derived by acquiring two calibration frames. A simple procedureis to photograph within the medium images of a black board. In oneframe, the board is placed at a distance Z₁ from the camera 10, while inthe second one it is placed at a distance Z₂. Since the object is black,the two frames measure only backscatter accumulated up to theirrespective depthsI _(i)(x,y)=B _(∞)(x,y){1−e^(−k(xy)[Z) ^(i) ^(−Z) ⁰ ^((x,y)])},  (13)for iε{1, 2}. These are two nonlinear equations with two unknowns. Bysetting Z₁ and Z₂ close to the camera 10, a first order approximation([1−exp(−η)]≈η) yields

$\begin{matrix}{{{\hat{Z}}_{0} = \frac{{I_{1}Z_{2}} - {I_{2}Z_{1}}}{I_{1} - I_{2}}},{\hat{k} = {\frac{I_{1} - I_{2}}{B_{\infty}\left( {Z_{1} - Z_{2}} \right)}.}}} & (14)\end{matrix}$

Our simulations showed that {circumflex over (Z)}₀ is insensitive to thecolor channel. This is expected, since it has a geometric meaning: theintersection of the LOS with the effective boundary of the illumination.We stress that this approximation (Eq. 12) is useful in scene recovery,as detailed in Sec. 5. To demonstrate the effectiveness of theparametric approximation, we performed this parameter calibration, andthen used Eq. (12) to render backscatter in scenes. The result is almostindistinguishable from that obtained by numeric integration ofbackscatter derived from first principles.

5 Scene Reconstruction

We wish to overcome the visibility degradation, and also to estimate a3D map of the scene. The method has two steps. The first is acquisitionusing active polarized-illumination and a camera 10 mounted polarizer40. The second is image analysis. We now describe the principles as wellas embodiments of the system.

5.1 Taking the Plunge

The experiments were done while scuba diving at night in variousenvironments, as described above. To observe color effects in theimages, we prepared colorful patch-targets and took them with us. Thecamera 10 was mounted on a tripod with weights on. To safely sink andfloat this amount of equipment in a dive, we used a lift bag as shown inFIG. 5.

Other studies have experimented with indoor water tanks, diluting afixed substance, usually milk. The particles in milk and other lipidsubstances are usually homogenic and symmetric [G. Jarry, E. Steimer, V.Damaschini, M. Epifanie, M. Ju-rczak, and R. Kaiser. Coherence andpolarization of light propagating through scattering media andbiological tissues. App. Opt., 37:7357-7367, 1998; V. Sankaran, J. T.Walsh, and D. J. Maitland. Comparative study of polarized lightpropagation in biologic tissues. J. Biomed. Opt., 7:300-306, 2002] whileoceanic particles are heterogeneous [C. D. Mobley. Light and Water:Radiative Transfer in Natural Waters, chapter 3,5. San-Diego: AcademicPress, 1994]. Therefore, we were concerned that polarization experimentsdone with milk would not represent correctly the properties of the mediain the field, e.g., seawater. Thus, we embarked on outdoor dives.

5.2 Image Acquisition

An example of a system setup is depicted in FIGS. 2 and 6. Polarizers 40are mounted on the sources while a polarizer 40 is mounted on the camera10 (analyzer 20). The polarizers 40 are either both linear or bothcircular [G. D. Gilbert and J. C. Pernicka. Improvement of under watervisibility by reduction of backscatter with a circular polarizationtechnique. App. Opt., 6:741-746, 1967] polarizers 40. Note that it ismore difficult to switch states (handedness) of circular polarizationthan to switch linear orthogonal states. Anyway, images are taken withthe analyzer 20 in two orthogonal polarization states. The first stateis chosen to be the one with minimum visible backscatter, denotedI^(min). The second state has maximum backscatter, denoted I^(max).Another option is to take one image with an analyzer 20 mounted on theimaging device (either I^(min) or I^(max)), and one without an analyzer20 at all, denoted I^(tot). The 2^(nd) polarization state can then becalculated using Eq. (16). Practically, an image without a polarizer 40or analyzer 20 can be viewed as a special case of a polarizationsetting/state.

We used a Nikon D100 camera 10, which has a linear response [Y. Y.Schechner and N. Karpel. Recovery of underwater visibility and structureby polarization analysis. IEEE J. Oceanic Eng., 30:570-587, 2005]. Thecamera 10 was placed in a Sealux underwater housing. We also usedAquaVideo light sources, with 80 W Halogen bulbs. Reasons for thisselection are detailed in the Appendix. As described in the following,we often measured a significant DOP of backscatter in experiments.Therefore, sometimes even the single I_(min) image results in a dramaticimprovement.

5.3 Backscatter Removal

Often, substantial backscatter is resistant to optical filtering.Further reduction of backscatter is achieved by post processing I_(min)and I_(max). As discussed in Sec. 2.3, the backscatter has a certainDOP, so its contribution varies among the two frames. Since in Sec. 4the signal is assumed to be unpolarized, the images we take areI ^(min) =S/2+B ^(min) , I ^(max) =S/2+B ^(max),  (15)where B^(min) and B^(max) are the backscatter intensities in therespective polarization filtered images. Without a polarization analyzer20, the image acquired would have beenI ^(tot) =I ^(min) +I ^(max)  (16)The DOP of the backscatter is

$\begin{matrix}{{p\left( {x,y} \right)} = {\frac{B^{{ma}\; x} - B^{m\; i\; n}}{B}.}} & (17)\end{matrix}$

If we know p(x, y), then using Eqs. (15,17) the backscatter in everypoint can be calculated as

$\begin{matrix}{{B\left( {x,y} \right)} = {\frac{{I^{{ma}\; x}\left( {x,y} \right)} - {I^{m\; i\; n}\left( {x,y} \right)}}{p\left( {x,y} \right)}.}} & (18)\end{matrix}$Here we make another assumption:

-   -   Uniform DOP of backscatter—In experiments we made in various        underwater environments and in different periods, we noticed a        surprisingly simple behavior: the DOP of the accumulated        backscatter is practically constant across the FOV despite the        angular spread of the illumination and views. Thus p(x, y)=p. We        found it is constant up to ≈24° relative to the optical axis.

We extract the DOP directly from the images. Note that in areas wherethere is no object, I^(tot)=B=B_(∞). Therefore, we can choose an area inthe image where no object exists, and then extract the DOP from theimage using Eq. (17). Alternatively, it can be taken in the calibrationstep of B_(∞) (x, y). Based on p and Eq. (18), we estimate thebackscatter and then remove it from the raw imageS(x,y)=I ^(tot)(x,y)−B(x,y).  (19)The backscatter removal results in a more uniform brightness, decreasingdynamic range problems. This enables better contrast and brightnessrange across the FOV.

FIG. 1 shows an unpolarized image taken with our system in theMediterranean, with sea conditions of approximately 8 m visibility. Herewe used two light sources placed 10 cm above and below the LOS. Theestimated DOP in this case was 80%. The backscatter greatly degradesvisibility, and its non-uniformity creates dynamic range problems. FIG.7A shows the result of applying Eqs. (18,19) on the scene shown in FIG.1, while FIG. 7B shows the estimated backscatter. There is a significantimprovement of visibility compared to the raw frame. Note the revealedrocks in the upper left and bottom, the sand in the periphery and thedistant tube region.

FIGS. 8A-D show an image taken in the fresh water Sea of Galilee withpoor visibility of about 0.5 m (which imposed significant inconvenienceduring the experiment). In this setup we used one light source, whichwas placed 10 cm above the LOS. The resulting circular DOP was 9%. Theimaged bucket is of the same size as the one shown in FIG. 7, just muchcloser. Despite its proximity, its rear edge is not visible in the rawimages. In contrast, after applying Eqs. (18, 19) to the circularpolarization pair, the rear edge is unveiled (though blurred). Thedarkness above that edge correctly indicates the void above and behindthe bucket. FIG. 8A shows an unpolarized image, FIG. 8B shows a bestpolarized image, FIG. 8A shows an image with backscatter removedaccording to the invention, and FIG. 8A shows the estimated backscatter.

5.4 Falloff Estimation

As discussed in Sec. 2.1, the amount of backscatter in each pixel isrelated to the distance of the corresponding object. The farther it is,the more backscatter accumulates along the LOS. In the previous section,we extracted the backscatter map, which indicates the object distance,i.e., the 3D structure of the scene. Furthermore, having thisestimation, we can somewhat compensate for the falloff. The depth valuesare derived from Eq. (12):

$\begin{matrix}{{{\hat{Z}}_{obj}\left( {x,y} \right)} = {{Z_{0}\left( {x,y} \right)} - {\left\lbrack {\ln\left( {1 - \frac{B\left( {x,y} \right)}{B_{\infty}\left( {x,y} \right)}} \right)} \right\rbrack/{{k\left( {x,y} \right)}.}}}} & (20)\end{matrix}$The parameters k(x, y) and Z₀(x, y) are calibrated as explained in Sec.4.

One should be aware of the limitation of this approach for 3D recovery.For example, FIG. 4 shows the result of a numeric calculation of B(z)using Eq. (10). In the first half a meter the backscatter increases at ahigh rate. Therefore, estimating distances in this range can bemeaningful. On the other hand, after a distance of about 1 m thebackscatter saturates. Hence trying to distinguish distances there isfruitless. The effective range can be increased to 2-3m when thebaseline or the attenuation coefficient change.

After estimating {circumflex over (Z)}_(obj)(x,y) in Eq. (20), it cannow be used for estimating the falloff. For this, we need theattenuation coefficient c, which can be evaluated by a transmissiometer.In addition, we need R_(source), which is derived based on a-prioriknowledge about the system baseline: as in [B. Sun, R. Ramamoorthi, S.Narasimhan, and S. Nayar. A practical analytic single scattering modelfor real time rendering. ACM TOG, 24:1040-1049, 2005], it is sufficientto know camera 10 light-source baseline R_(sc), and the angle betweenthis source and the LOS, γ (See FIG. 2). Then,R _(source)=√{square root over (R _(sc) ² +R _(cam) ²−2R _(cam) R _(sc)cos γ)}.  (21)The value of {circumflex over (R)}_(cam) is estimated by settingz=Z_(obj) in Eq. (4). Then Eq. (21) derives {circumflex over(R)}_(source). Using them in Eq. (6), we get the estimated falloff{circumflex over (F)}(x, y). The latter can be compensated for (see Eq.7):{circumflex over (L)} _(object)(x,y)=S(x,y)/{circumflex over(F)}(x,y).  (22)

FIG. 9 shows a typical dependence of F on B (both are normalized bytheir maximal value). We can see that the function is stable andestimation of falloff based on backscatter is well-conditioned.

FIGS. 10A-D show a simulation of the entire recovery method. The imagewas assigned a non-trivial distance map and artificial noise was addedwith standard deviation of 1 grey level (out of 256 in the image). FIG.10D shows the image after removal of the estimated backscatter andfalloff compensation. While the image is enhanced relative to theacquired image (FIG. 10B), there is noise amplification in the distantparts. The reconstructed distance map (FIG. 10C) matches the originalone (FIG. 10A).

6 Removing Backscatter Based on Known Distances

Out of preliminary knowledge of the scene structure (e.g. imaging in apipeline) we can know the backscatter value at each pixel. For example,it can be calibrated by imaging a black object with the same structure.Another way is to model the 3D structure and calculate the value out ofthe model for the backscatter and calibration of medium properties.Alternatively, note that when moving in a scene with a constantstructure, e.g. in a pipeline or in a constant height above ground, thebackscatter value is temporally invariant, and may thus be estimatedfrom an ordinary image sequence taken while moving in the structure.

Now, the backscatter value can be subtracted from every raw image toobtain a backscatter-free image. After this removal, the brightness ofthe image is more even and thus other image processing methods can beapplied.

A specific example is a scene containing objects with distances largerthan the effective backscatter saturation distance. This is easy tocalibrate-simply point the system to an area with no object. Then,B_(∞)(x, y) can be simply subtracted from the raw image taken in thescene.

7 Enhancing Specular Objects

The polarization based algorithm is based on the assumption that theobjects reflect depolarized light. However, in the case of a specular orpolarizing objects, other methods such as polarization differenceimaging [J. S. Tyo, M. P. Rowe, E. N. Pugh, and N. Engheta. Targetdetection in optically scattering media by polarization-differenceimaging. App. Opt., 35:1855-1870, 1996] may work better. Many scenescontain both types of objects. We may thus have two resulting images athand: one is a result of the method described in section 5. The otherimage is a result of methods tuned to polarizing objects. We can combinethe two results (or more) by various methods of image fusion. An exampleis the image fusion method described in [A. Agrawal, R. Raskar, S.Nayar, and Y. Li. Removing photography artifacts using gradientprojection and flash-exposure sampling. In Proc. ACM SIGGRAPH, 2005].This would enhance both specular objects and diffuse objects.

8 Discussion

Our approach is instant, easy to build and cheap. It is a physics-basedenhancement of contrast. The method is general enough and it can workeven if not all the assumptions are true. The method of the inventioncan also yield a rough estimate of the 3D scene structure. Note that 3Dreconstruction can be done mostly in short ranges, where the backscatterexpression still varies rapidly and light still exists with sufficientintensity. On the other hand, visibility recovery is achieved throughoutthe range of the light source without limit. The practical limit ofhaving less light reaching distant objects is fundamental to all activeillumination methods.

The method of the invention can be combined with spatial/temporal scanmethods. Scanners [G. R. Fournier, D. Bonnier, L. J. Forand, and P. W.Pace. Range-gated underwater laser imaging system. Opt. Eng,32:2185-2190, 1993] can use lasers which generate polarized light bystimulated emission [E. Hecht. Optics, chapter 8,13. Addison Wesley, 4thedition, 2002] without loss, while projectors [M. Levoy, B. Chen, V.Vaish, M. Horowitz, I. McDowall, and M. Bolas. Synthetic apertureconfocal imaging. ACM TOG, 23:825-834, 2004; S. G. Narasimhan, S. K.Nayar, B. Sun, and S. J. Koppal. Structured light in scattering media.In Proc. IEEE ICCV, volume 1, pages 420-427, 2005] often emit polarizedlight [M. Robinson, G. Sharp, and J. Chen. Polarization Engineering forLCD Projection. Wiley, 2005].

9 Visibility Enhancement in Scattering Media Using Fusion

In another aspect, the present invention relates to a method forvisibility enhancement in scattering media with artificial and/ornatural illumination, by using fusion techniques. In such media imagessuffer from two dominant problems: 1. Backscatter—veils the object; and2. Attenuation of light—causing limited visibility range and unevenscene illumination.

Those two effects cause the image to have high dynamic range problem.Some parts that are veiled by the backscatter may be almost invisible,and the parts that are not veiled may have relative low intensity. As aresult, traditional image processing methods like contrast stretch mayhave a limited effect.

The fusion method of the invention aims to solve this problem. Wesuggest using two or more images of the same scene. The images should bedifferent in their illumination. This can be achieved either by movingthe light source, by using different light sources located in differentplaces, by moving the camera 10 or any combination thereof.Specifically, we found that even a simple configuration of using onesource at the top of the camera 10 and the second in the bottom yieldsexcellent results. The acquired set of images is used to construct agood image of the scene.

The result is achieved by combining information from all the imagesusing a quality criterion. In one embodiment of the present invention,the method of image fusion uses laplacian pyramid decompositionfollowing [Peter J. Burt and Edward H. Adelson. The laplacian pyramid asa compact image code. IEEE Transactions On Communications,Com-31(4):532{540, April 1983]. In this decomposition, two pyramids areconstructed for each image—the gaussian and the laplacian, denoted G_(i)and L_(i) accordingly. The level is indicated by the i index. The baselevel of the pyramid is defined as the level corresponding to the lowestspatial frequencies. As a result, the base level has the lowestresolution.

9.1 The Method Steps

1. Decompose each image into a gaussian and a laplacian pyramid,according to the description in [Peter J. Burt and Edward H. Adelson.The laplacian pyramid as a compact image code. IEEE Transactions OnCommunications, Com-31(4):532{540, April 1983]. The maximum level N is aparameter. We got best results setting N such that the base level sizeis approximately 4 pixels by 4.

2. Create a new laplacian pyramid, in which each level is composed ofvalues from the corresponding level in the laplacian pyramids of all theimages. The decision process is described in 9.2.

3. The base level is created using the base levels of the pyramids,using a different decision method, described in 9.3.

4. Decode the final image using the new pyramid.

9.2 Decision Making in Each Level

Various criterion functions exist in the literature. We found the onedescribed in [A. Toet. Image fusion by a ratio of low pass pyramid.Pattern Recognition Letters, 9:245{253, 1989] to fit our problem best,although other methods can be used as well.

Suppose we have M frames. For each frame we compute another pyramid, acontrast pyramid. We start by computing a ratio of low pass pyramid,R_(i) for each frame:R _(i) =G _(i)/expand[G _(i+1)].  (23)The expand action is defined in [Peter J. Burt and Edward H. Adelson.The laplacian pyramid as a compact image code. IEEE Transactions OnCommunications, Com-31(4):532{540, April 1983]. This follows thedefinition of luminance contrast as:

$\begin{matrix}{\frac{{local}\mspace{20mu}{contrast}}{{background}\mspace{20mu}{contrast}} - 1.} & (24)\end{matrix}$Therefore, the contrast pyramid C_(i) is defined byC _(i) =R _(i)−1.  (25)Then, the contrast pyramid helps to construct the new laplacian pyramid:

$\begin{matrix}{{{L_{i}\left( {x,y} \right)} = {L_{i,k}\left( {x,y} \right)}},{k = {\underset{j}{\arg\mspace{14mu}\max}{\left( {{C_{i,j}\left( {x,y} \right)},{j \in \left\lbrack {1,M} \right\rbrack}} \right).}}}} & (26)\end{matrix}$Here we added a second index kε[1,M] to the laplacian pyramid notation,which denotes the frame index. The decision can be different for eachpixel, and therefore its location is denoted by (x, y).9.3 Base Level

In various image fusion applications, the base level is usually combinedby averaging the base levels or taking their maximum. We found out thatthose methods retain the non-uniform illumination so we suggest adifferent method. We assign the base level a constant value which is theaverage of all pixel values of all base levels. This action eliminatesthe low frequencies, leaving only a DC level. This idea is similar tohomomorphic filtering [B. Johnston, M. S. Atkins, B. Mackiewich, and M.Anderson. Segmentation of multiple sclerosis lesions in intensitycorrected multispectral mri. Ieee Transactions On Medical Imaging,15(2):154{169, April 1996]. Low frequencies are usually associated toillumination in the scene. Therefore, replacing them with only a DCresults in even illumination. However, this method works only if thepyramid level is chosen carefully, as suggested in 9.1. If the pyramidlevel is not deep enough, the resulting image is gray.

9.4 Why this Method Works

There are two key ideas:

-   -   1. Eliminating low frequencies makes the illumination even, and        therefore enhances the details, even when applied to a single        image.    -   2. When using different images of the same scene, each area has        an image where it has the best contrast. Combining information        using an appropriate criterion results in getting the best        contrast for each area.        Backscatter Removal by Polarization-Extension to Polarized        Objects        10 Model and Algorithm

Former studies have used polarized illumination for backscatter removal.In [T. Treibitz and Y. Y. Schechner. Instant 3descatter. In Proc. IEEEComputer Soc. Conf. on Computer Vision and Pattern Recognition, pages1861 {1868, 2006] we assumed that the objects back-reflect unpolarizedlight to the camera 10. On the other hand, Polarization DifferenceImaging (PDI) assumes that p_(obj)

p_(∞) [J. S. Tyo, M. P. Rowe, E. N. Pugh, and N. Engheta. Targetdetection in optically scattering media by polarization-differenceimaging. App. Opt., 35:1855{1870, 1996]. Here we develop a generalizedmodel, not requiring assumptions on the polarization of the objects.Fortunately, if the object yields polarized specular reflection, itbehaves similarly to the backscatter: out of the two frames, generally,the one in which the backscatter is brighter is also the one in whichthe object back-reflection is brighter. In water, specular (rather thandiffuse) reflection has the potential of strongly reflecting polarizedlight from a polarized source. Empirically, we never encountered areversed polarization of the signal relative to the backscatter. Notethat some studies [J. S. Taylor, Jr., and L. B. Wolff. Partialpolarization signature results from the field testing of the shallowwater real-time imaging polarimeter (SHRIMP). In Proc. MTS/IEEE OCEANS,volume 1, pages 107{116, 2001; J. S. Tyo, M. P. Rowe, E. N. Pugh, and N.Engheta. Target detection in optically scattering media bypolarization-difference imaging. App. Opt., 35:1855{1870, 1996] assumethe opposite—that the signal is polarized, ignoring the backscatterpolarization.

As described in [T. Treibitz and Y. Y. Schechner. Instant 3descatter. InProc. IEEE Computer Soc. Conf. on Computer Vision and PatternRecognition, pages 1861{1868, 2006], we take two images of the samescene using two orthogonal polarization states of the polarizer 40. Hadthe backscattered light completely retained its polarization, it couldhave been optically eliminated by the analyzer 20. We discovered that asubstantial DOP is maintained upon backscattering. We exploit thisphenomenon (Polarization has also aided other computer vision aspects[M. Ben-Ezra. Segmentation with invisible keying signal. In Proc. IEEECVPR, volume 1, pages 32{37, 2000; O. G. Cula, K. J. Dana, D. K. Pai,and D. Wang. Polarization multiplexing for bidirectional imaging. InProc. IEEE CVPR, volume 2, pages 1116{1123, 2005; H. Farid and E. H.Adelson. Separating reflections and lighting using independentcomponents analysis. In Proc. IEEE CVPR, volume 1, pages 262{267, 1999;D. Miyazaki and K. Ikeuchi. Inverse polarization raytracing: estimatingsurface shape of transparent objects. In Proc. IEEE CVPR, volume 2,pages 910{917, 2005; Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar.Instant dehazing of images using polarization Proc. IEEE CVPR,1:325{332, 2001; L. B. Wolff. Polarization vision: a new sensoryapproach to image understanding. Image & Vision Comp., 15:81{93, 1997]).Consequently, placing an analyzer 20 in the orthogonal state to thebackscatter's polarization state yields an image with minimum visiblebackscatter. We denote this image as I_(min). Imaging with the oppositeorthogonal state, denoted I^(max), has the maximum backscatter. Asdescribed in the following, we often measured a significant DOP ofbackscatter in experiments.

A general image in a scattering medium can be expressed as:I(x _(obi))=S(x _(obj))+B(x _(obj)).  (27)where B is the backscatter component, S is the attenuated signal andx_(obj) is the pixel coordinate. As a result, the image pair consistsof:I _(max() x _(obj))=S _(max() x _(obj))+B _(max() x _(obj)). I _(min() x_(obj))=S _(min() x _(obj))+B _(min() x _(obj))  (28)We define the degrees of polarization (DOPs) p_(obj) and p_(∞) of thesignal and the backscatter accordingly:

$\begin{matrix}{{{p_{obj}\left( x_{obj} \right)} = \frac{{S_{{ma}\; x}\left( x_{obj} \right)} - {S_{m\; i\; n}\left( x_{obj} \right)}}{{S_{{ma}\; x}\left( x_{obj} \right)} + {S_{m\; i\; n}\left( x_{obj} \right)}}},{{p_{\infty}\left( x_{obj} \right)} = \frac{{B_{{ma}\; x}\left( x_{obj} \right)} - {B_{m\; i\; n}\left( x_{obj} \right)}}{{B_{{ma}\; x}\left( x_{obj} \right)} + {B_{m\; i\; n}\left( x_{obj} \right)}}}} & (29)\end{matrix}$In the following we omit the (x_(obj)) for clarity. We end up with twoequations for the two scene unknowns −S and B:I _(max) +I _(min) =B+S  (30)I _(max) −I _(min) =p _(∞) B+p _(obj) S.  (31)The last equation is derived from plugging Eq. (29) in Eq. (28). Thesolution to this equation set is:

$\begin{matrix}{\hat{S} = {\frac{1}{p_{\infty} - p_{obj}}\left\lbrack {{I_{m\; i\; n}\left( {1 + p_{\infty}} \right)} - {I_{{ma}\; x}\left( {1 - p_{\infty}} \right)}} \right\rbrack}} & (32) \\{\hat{B} = {{\frac{1}{p_{\infty} - p_{obj}}\left\lbrack {{I_{{ma}\; x}\left( {1 - p_{obj}} \right)} - {I_{m\; i\; n}\left( {1 + p_{obj}} \right)}} \right\rbrack}.}} & (33)\end{matrix}$

This is a general result, enabling separation of B and S from the tworaw images, given the DOPs p_(obj) and p_(∞).

A very important property of Eq. 32 is that p_(obj) contributes only ascale factor in the signal reconstruction. Therefore, if p_(obj) isapproximately constant across the scene, the signal estimation is trueup to a scale even when ignoring p_(obj). For purposes of visibilityenhancement this is more than enough. The backscatter is removed, andmissing parts are revealed. Furthermore, the resulting image has asmaller dynamic range. Thus, applying standard image enhancementtechniques usually results in a further image improvement in contrary toapplying those techniques on the raw images. As a consequence, manyprevious works [Y. Y. Schechner and N. Karpel. Recovery of underwatervisibility and structure by polarization analysis. IEEE J. of OceanicEng., 30:570{587, 2005; Y. Y. Schechner, S. G. Narasimhan, and S. K.Nayar. Polarization-based vision through haze. App. Opt., 42:511 {525,2003; T. Treibitz and Y. Y. Schechner. Instant 3descatter. In Proc. IEEEComputer Soc. Conf. on Computer Vision and Pattern Recognition, pages1861 {11868, 2006; J. G. Walker, P. C. Y. Chang, and K. I. Hopcraft.Visibility depth improvement in active polarization imaging inscattering media. App. Opt., 39:4933{4941, 2000] achieved very goodresults based on this assumption. In this case Eq. (32) reduces to:Ŝ=[I _(min)(1+p _(∞))−I _(max)(1−p _(∞))]/p_(∞)  (34){circumflex over (B)}(x,y)=(I _(max) −I _(min))/p _(∞).  (35)Using Eq. (35) when p_(obj)≠0 yields a false estimation, {tilde over(B)}:

$\begin{matrix}{\overset{\sim}{B} = {\frac{I_{{ma}\; x} - I_{m\; i\; n}}{p_{\infty}} = {{\hat{B} + \frac{S_{{ma}\; x} - S_{m\; i\; n}}{p_{\infty}}} = {\hat{B} + {\frac{p_{obj}}{p_{\infty}}{S.}}}}}} & (36)\end{matrix}$

The last equality results from plugging in the DOP p_(obj) from Eq.(29). As explained in [T. Treibitz and Y. Y. Schechner. Instant3descatter. In Proc. IEEE Computer Soc. Conf. on Computer Vision andPattern Recognition, pages 1861{1868, 2006], B increases with distancewhereas S decreases with the distance. A result of Eq. (10) is that{circumflex over (B)} is no longer monotonic with Z_(obj).

Some methods assume the opposite: p_(∞)/p_(obj)≈0. Those are calledPolarization Difference Imaging (PDI) [J. S. Tyo, M. P. Rowe, E. N.Pugh, and N. Engheta. Target detection in optically scattering media bypolarization-difference imaging. App. Opt., 35:1855{1870, 1996].Plugging this assumption to the above equations results in:

$\begin{matrix}{{\hat{S} = {\frac{1}{p_{obj}}\left\lbrack {I_{{ma}\; x} - I_{m\; i\; n}} \right\rbrack}},} & (37) \\{\hat{B} = {{\frac{1}{p_{obj}}\left\lbrack {{I_{m\; i\; n}\left( {1 + p_{obj}} \right)} - {I_{m\;{ax}}\left( {1 - p_{obj}} \right)}} \right\rbrack}.}} & (38)\end{matrix}$

Note that in this case, Eq. (37) is a scaled version of the polarizationdifference image used in PDI.

Sec. 11 describes estimating the DOPs in the general case. First we showsome results and introduce a 3D reconstruction approach.

11 Estimating p_(obj)

The need for an estimation for p_(obj) arises when trying to estimatedistances based on the wrong estimation of the backscatter, as describedin [T. Treibitz and Y. Y. Schechner. Instant 3descatter. In Proc. IEEEComputer Soc. Conf. on Computer Vision and Pattern Recognition, pages1861 {1868, 2006]. We want to emphasize that compared to scenes takenunder natural illumination [Y. Y. Schechner and N. Karpel. Recovery ofunderwater visibility and structure by polarization analysis. IEEE J. ofOceanic Eng., 30:570{587, 2005; Y. Y. Schechner, S. G. Narasimhan, andS. K. Nayar. Polarization-based vision through haze. App. Opt.,42:511{525, 2003], here the correct approximation of p_(obj) is moreimportant for using the backscatter for distance estimation. Undernatural illumination the objects are usually further away, the lightthat hits them is usually only partially polarized and even if they backreflect polarized light, it has a low polarization degree and itdepolarizes on the way to the camera 10. Under polarized artificialillumination conditions are usually different. The light that hits theobjects usually has a higher degree of polarization and the imagedobjects are much closer to the camera 10. Thus, there are cases when thelight intensity that reaches the camera 10 from the objects has aconsiderable amount of polarization. Moreover, p_(obj) decreases withobject distance. For example, in the scenes we present in the following,the rocks, which are usually considered unpolarizing, were ≈30%polarized. Failing to estimate p_(obj) correctly damages the monotonicrelation between the estimated backscatter and the object distance.FIGS. 13A-B demonstrate that.

FIGS. 13A-B present an image of {circumflex over (B)}/B_(∞) for anunderwater scene. FIG. 13A assumes p_(obj)=0. FIG. 13B: Using anestimated p_(obj). In FIG. 13A areas in proximity to the camera 10(lower part of the image) are falsely assigned a high value unlike thecorrect low values in FIG. 13B. Assuming p_(obj) is constant across thescene, areas that do not comply to this assumption damage themonotonicity of {circumflex over (B)}/B_(∞)(Z_(obj)) (blue ellipses).

FIG. 13A shows the calculated relation B_(rel) with the assumption thatp_(obj)=0. We can see that the entire image has approximately the samevalue no matter what the object distance is. On the other hand, theimage taking into consideration p_(obj) has a clear dependency on objectdistance—the closer front part and the left rock are darker. Thus it isbetter not to ignore p_(obj). There are some cases when p_(obj) can besampled directly from the scene. When the light source lights from oneside of the FOV to another, the objects in the far end are lit but nobackscatter reaches the camera 10 (like in [S. G. Narasimhan, S. K.Nayar, B. Sun, and S. J. Koppal. Structured light in scattering media.In Proc. IEEE ICCV, volume 1, pages 420{427, 2005]). For example, thelike red circled area in FIG. 14A. When sampling areas like this one I=Sand

$\begin{matrix}{p_{obj} = {\frac{{I_{{ma}\; x}\left( {{clear}\mspace{25mu}{area}} \right)} - {I_{m\; i\; n}\left( {{clear}\mspace{20mu}{area}} \right)}}{{I_{{ma}\; x}\left( {{clear}\mspace{20mu}{area}} \right)} + {I_{m\; i\; n}\left( {{clear}\mspace{20mu}{area}} \right)}}.}} & (39)\end{matrix}$The measured values were p_(obj) [R, G, B]=[0.22, 0.27, 0.34].

Nevertheless, we present here a general automatic approach for that. Itis based on the observation that using a wrong value for p_(obj) resultsin a high cross-correlation between the backscatter and the signalcomponents. Artifacts from the object signal can actually be seen in thebackscatter estimation. Therefore, seeking for the value that minimizesthe mutual information between both components results in the value ofp_(obj) we are looking for.

In FIGS. 14A-D we can see an example of an underwater scene. FIG. 14A isa scene with a polarized reflection from an object. FIG. 14B is an imagewherein the value of {circumflex over (B)} is extracted assumingp_(obj)=0. FIG. 14C shows B_(∞), FIG. 14D is an image of {circumflexover (B)}, using an estimated value of p_(obj), using minimization ofthe mutual information. FIG. 14E is a graph of the mutual informationbetween {circumflex over (B)} and Ŝ in each channel (R, G, B), usingdifferent values for p_(obj).

FIG. 14A shows the raw scene. Notice that the illumination comes fromthe bottom right corner of the FOV, and thus the rock in the top leftpart of the image (circled) is clearly lit but has no backscatter.Calculating the backscatter with the assumption that p_(obj)=0 resultsin a backscatter image with a high value in FIG. 14B. The rock isclearly seen there. Compared to the B_(∞) image FIG. 14C we see anunreasonable amplification of the backscatter in this part, as if it wasvery far. FIG. 14D shows the correct estimation of the backscatter—it isalmost zero in this part. In the right side of FIG. 14 we can see themutual information calculated between the signal and the backscattercomponents for different values of p_(obj). We get minima, a slightlydifferent one for each color channel. The values are almost identical tothe sampled values as given above. Note, that once the DOP of a fewknown materials like rocks, sand, metals, etc., is known, it can beapplied to different parts in the image without the need to recalculateit.

The problem becomes more complicated when the DOP of the objects variesacross the scene. In FIG. 13B we can see (in blue ellipses) two objectswith a significantly different DOP than the rest of the scene. It causesdistortions in backscatter image. In this case, we assigned thoseobjects their exact DOP (0) in order to get an estimation of thedistance map shown in FIG. 15. Let us calculate what will be the errorin B using a wrong value for {tilde over (p)}_(obj)=p_(obj)+d, where dis the error.

$\begin{matrix}{\overset{\sim}{B} = {{\frac{1}{p_{\infty} - p_{obj} - d}\left\lbrack {{I_{{ma}\; x}\left( {1 - p_{obj} - d} \right)} - {I_{m\; i\; n}\left( {1 + p_{obj} + d} \right)}} \right\rbrack} =}} & (40) \\{{\frac{1}{p_{\infty} - p_{obj} - d}\left\lbrack {{I_{{ma}\; x}\left( {1 - p_{obj}} \right)} - {I_{m\; i\; n}\left( {1 + p_{obj}} \right)} - {d\left( {I_{{ma}\; x} - I_{m\; i\; n}} \right)}} \right\rbrack} =} & (41) \\{{\frac{p_{\infty} - p_{obj}}{p_{\infty} - p_{obj} - d}\hat{B}} - {{\frac{d}{p_{\infty} - p_{obj} - d}\left\lbrack \left( {I_{{ma}\; x} - I_{m\; i\; n}} \right) \right\rbrack}.}} & (42)\end{matrix}$We can see that overestimating p_(obj) (d>0) results in a lowerbackscatter component. This can be seen in the area marked with the bluecircles in FIG. 13B. In those parts p_(obj)≈0 and thus they appeardarker than their environment. Moreover, because p_(obj) varies in thecolor channels, they appear colored. On the other hand, underestimatingp_(obj) (d<0) results in a higher backscatter-like seen in FIG. 14B.12 Calibration of Backscatter Approximation Parameters

As discussed earlier to calibrate the backscatter approximationparameters, we need values of the backscatter in two close distances tothe camera 10. There are a few ways to achieve that:

-   -   1. Imaging a total absorbing black board in two distances.    -   2. Imaging two different boards in two distinct distances. The        ratio between the albedos of the boards needs to be known        a-priori. This is useful when an absorbing board is unavailable.    -   3. The polarization method can also be used to extract the        backscatter. Care need to be taken not to use a material that        reflects polarized light. This is sometimes hard to achieve.        12.1 Extracting Backscatter from Image of Two Boards

In every image in a scattering medium the acquired image I is composedof two components:I=D+BS  (43)where D is the direct transmission component and BS is the backscattercomponent. The direct component is the signal which is reflected fromthe illuminated object, attenuated according to the medium propertiesand its location relative to the camera 10 and to the light source.

$\begin{matrix}{D = {I_{0}a_{i}\frac{\exp\left\lbrack {- {\beta\left( {R_{c} + R_{s}} \right)}} \right\rbrack}{R_{S}^{2}}}} & (44)\end{matrix}$where: I₀ is the light source intensity, a_(i) the albedo, β the mediumattenuation coefficient, R_(c) the object distance from camera 10 andR_(s) the object distance from the light source. In general, they canvary for each pixel. Let us look at the specific case of imaging twoboards with different albedos, located at the same distance from thecamera 10. Except of the albedo, the rest of the parameters in thedirect transmission component are constant. Therefore, using Eq. (43),we can express the ratio of both direct components (D₁,D₂) as:

$\begin{matrix}{{{\alpha \doteq \frac{D_{1}}{D_{2}}} = {\frac{a_{1}}{a_{2}} = \frac{I_{1} - {BS}}{I_{2} - {BS}}}},} & (45)\end{matrix}$where I₁, I₂ are the two raw images. From Eq. (45) we can extract thebackscatter component:

$\begin{matrix}{{BS} = {\frac{I_{1} - {\alpha\; I_{2}}}{1 - \alpha}.}} & (46)\end{matrix}$Assuming α is known, we get the backscatter. This process is done foreach distance so we end up having two backscatter images that are usedfor calibration.12.2 Attenuation Coefficient Extraction

After separating both image components, we can use the directtransmission component to estimate the medium attenuation coefficient.

$\begin{matrix}{\frac{D_{1}}{D_{2}} = {\frac{R_{s_{2}}^{2}}{R_{s_{1}}^{2}}{{\exp\left\lbrack {- {\beta\left( {R_{c_{1}} - R_{c_{2}} + R_{s_{1}} - R_{s_{2}}} \right)}} \right\rbrack}.}}} & (47)\end{matrix}$All the parameters except of β are known and therefore we can extractit. Note that β is constant over the image and therefore we need to knowonly a small number of distances in order to extract it.Appendix: Illumination Choices

An embodiment of the system is shown in FIG. 6. It consists of a lightsource; a diffuser 50 to make the light beam more uniform and widen itsspread; a polarizer 40 for the light source; an SLR camera 10 with anunderwater housing; and a polarizer 40 mounted on the camera 10. Theconsiderations for choosing a camera 10 and a housing in conjunction topolarization filtering are detailed in [Y. Y. Schechner and N. Karpel.Recovery of underwater visibility and structure by polarizationanalysis. IEEE J. Oceanic Eng., 30:570-587, 2005]. As for theillumination, we had several requirements, beyond being watertight inthe underwater depth, as detailed below.

-   Stability: We had to avoid uncontrolled illumination fluctuations in    this research phase. This has overruled current arc-based flash    bulbs, which have    (5%) fluctuations [Hamamatsu. Xenon ash lamps. Catalog TLSX1008E04    (Hamamatsu Photnics K.K., Electron Tube Center), 1998]. DC    incandescent sources are least prone to short-term fluctuations,    once their temperature saturates.-   Narrow lamphead exit aperture enables fitting high quality filters.    This has overruled current large LED clusters or fluorescent bulbs.-   Holographic diffusers 50 are used for higher transmission efficiency    and smaller diffusing angles.-   Sealed diffuser. High efficiency diffusers 50 are either    ground/sandblusted glass or holographic. The former become clear    (nondiffusing) in water, as their refractive index is nearly matched    by water in their concavities. The latter are destroyed in water.    Thus, we sealed the diffusers 50 in air spaced windows.-   Diffuser 50 before polarizer. Diffusers 50 scramble light, causing    depolarization. Lab tests verified a higher illumination DOP when    the diffuser 50 is placed between the polarizer 40 and the lamphead    30, rather than facing the object.-   High intensity extends the vision range in the water.-   Enough battery power to last for long underwater experiments with    fast recharging in field use.-   Creating a double-polarized light source. One can use a polarized    array of LEDs, where half of the LEDs are polarized perpendicular to    the other LEDs (see FIG. 11). Then, a simple switch turns on only    part of the LEDs such that different frames may have different    polarization of the illumination.-   Natural cooling. We attach the polarizer 40 and the diffuser 50 to    the light source, with a gap between the light source and the two    filters (see FIG. 12). The surrounding medium can fill-in the gaps,    providing natural cooling to the system.-   Light recycling. A standard polarizer 40 usually transmits only half    (or less) of the light intensity. We suggest using devices that    convert a larger proportion of the energy into polarized light. This    can be done using polarizing beamsplitters and retarders. It can    also be done using wire-grid polarizers 40, which reflect the    unpolarized light back into the light source reflector. Then, the    light not transmitted to the scene is recycled. This way, the    illumination in the scattering media is efficiently made polarized.

Although the invention has been described in detail, neverthelesschanges and modifications, which do not depart from the teachings of thepresent invention, will be evident to those skilled in the art. Suchchanges and modifications are deemed to come within the purview of thepresent invention and the appended claims.

1. An imaging method for recovering object visibility in a scenecontaining a scattering medium, said method comprising the steps of: (i)illuminating the scene with an active illumination system on which apolarizer is mounted; (ii) acquiring a first frame of the scene with animage acquisition equipment comprising a polarization analyzer; (iii)acquiring one or more additional polarized frames of the scene in adifferent polarization state of the polarizer or of the polarizationanalyzer or of both, or acquiring one or more additional unpolarizedframes of the scene; (iv) estimating the degree of polarization ofbackscatter in every point of said scene; and using a combination of allor part of the frames from (i)-(iii) and the analysis performed in (iv)to obtain one or more enhanced images with improved contrast andbrightness range across the field of view.
 2. An imaging methodaccording to claim 1, wherein said one or more additional frames of thescene are acquired with the polarizer or the polarization analyzer in apolarization state with approximately maximum or high visiblebackscatter; or wherein said first frame of the scene is acquired withthe polarizer or the polarization analyzer in a polarization state withapproximately minimum or low visible backscatter; or both.
 3. An imagingmethod according to claim 1, further compensating for signalattenuation.
 4. An imaging method according to claim 1, wherein saidenhanced image is further combined with one or more images obtained byany method adapted for enhancing images of polarizing objects.
 5. Animaging method according to claim 1, wherein said active illuminationsystem comprises at least one of the following: (i) a multi-polarizedlight source composed of a polarized array of light sources so that atleast one portion of the light sources are polarized in a differentpolarization state compared to the polarization state of the remaininglight sources, and at least two frames are acquired using differentpolarization of the illumination; (ii) one or more optical filtersattached to a light source with a gap between said light source and thepolarizer and analyzer so that the surrounding medium can fill in thegaps, providing natural cooling to the system; (iii) one or more devicesthat convert more than half the energy into polarized light ;or (iv) apolarization analyzer is mounted on part or all of the pixels of animaging sensor, so that the polarization analyzer mounted on one portionof the pixels is in one polarization state and the polarization analyzermounted on the remaining pixels of said imaging sensor is in one or moredifferent polarization states.
 6. An imaging method according to claim1, further estimating the distances between objects in said scene orfurther estimating and compensating for falloff or both.
 7. An imagingmethod according to claim 1, wherein said one or more additional framesof the scene are acquired without mounting a polarization analyzer onsaid image acquisition equipment.
 8. An imaging method for recoveringobject visibility of an object immersed in a scattering medium scene,said method comprising the steps of: (i) illuminating a scene in ascattering medium using an illumination system, wherein said scatteringmedium comprises water, fog or biological tissues; (ii) acquiring afirst frame of the scene with an image acquisition equipment; (iii)acquiring a second frame of either: an illuminated void region in saidscene, with no objects in sight; a black object in said scene; or acomputer simulation of the backscatter value at each pixel based onknowledge of the scene structure or an equivalent analyticalcalculation; and (iv) subtracting a portion or all of the second framefrom the first frame to obtain an enhanced image with improved contrastand brightness range across the field of view.
 9. An imaging methodaccording to claim 8, wherein said first frame is of a scene containingobjects with distances larger than the effective backscatter saturationdistance and said second frame is of an illuminated void region in saidscene, with no objects in sight or of a computer simulation of thebackscatter value at each pixel based on knowledge of the scenestructure or an equivalent analytical calculation.
 10. An imaging systemfor recovering object visibility in a scene containing a scatteringmedium, said system comprising: (i) means for illuminating the scenewith an active illumination system on which a polarizer is mounted; (ii)means for mounting a polarization analyzer on an image acquisitionequipment; (iii) means for acquiring a first frame of the scene; (iv)means for changing the polarization state of the polarizer or of thepolarization analyzer or of both; (v) means for acquiring one or moreadditional polarized or unpolarized frames of the scene; (vi) means forestimating the degree of polarization of backscatter in every point ofsaid scene; (vii) means for estimating the backscatter in every point ofsaid scene based on the analysis performed in (vi); and (viii) means fordeducting a portion or all of the value of said backscatter in eachpoint of said scene to obtain one or more enhanced images with improvedcontrast and brightness range across the field of view.
 11. An imagingsystem for recovering object visibility of an object immersed in ascattering medium scene, said system comprising: (i) means forilluminating a scene in a scattering medium using an illuminationsystem, wherein said scattering medium comprises water, fog orbiological tissues; (ii) means for acquiring a first frame of the scenewith an image acquisition equipment; (iii) means for acquiring a secondframe of either: an illuminated void region in said scene, with noobjects in sight; a black object in said scene; or a computer simulationof the backscatter value at each pixel based on knowledge of the scenestructure or an equivalent analytical calculation; and (iv) means forsubtracting a portion or all of the second frame from the first frame toobtain an enhanced image with improved contrast and brightness rangeacross the field of view.